Ratio Calculator
Simplify ratios, solve proportions, and split totals in a given ratio.
Calculation Type
Input Values
Mixing Calculator
Simplified Ratio
Original: 3:4
Step-by-Step Solution
As Decimal
3 ÷ 4
As Percentage
3 out of total
Mixing Results
Equivalent Ratios
How it works
A ratio compares two quantities. This calculator simplifies a ratio to its lowest terms (by dividing both sides by their greatest common divisor) and scales it up or down while keeping the proportion intact.
Simplify & scale a ratio
Simplify: divide a : b by gcd(a, b) Scale: a : b = (a·k) : (b·k)
- a : b
- the two parts of the ratio
- gcd
- greatest common divisor of a and b
Worked example
- Ratio 8 : 12
- gcd(8, 12) = 4
- 8 ÷ 4 : 12 ÷ 4
8 : 12 simplifies to 2 : 3.
Good to know
- A ratio a : b is the same proportion as the fraction a/b, so the same simplifying rules apply.
- To split a total in a ratio, add the parts (2 + 3 = 5) and give each its share of the whole.
- Equivalent ratios scale by the same factor on both sides.
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Frequently Asked Questions
How do I simplify a ratio?
Divide both sides by their greatest common divisor. For 8:12, the GCD is 4, so the ratio simplifies to 2:3. The same works with more than two parts — divide every part by the GCD of all of them.
How do I find a missing value in a proportion?
Set the two ratios equal and cross-multiply. If 2:3 = x:12, then 3x = 24, so x = 8. This is how you scale a recipe, a map distance, or a mixture while keeping the proportion intact.
How do I split an amount in a given ratio?
Add the ratio parts to get the total number of shares, divide the amount by that total, then multiply by each part. Splitting $500 in a 2:3 ratio gives 5 shares of $100 — so $200 and $300.
What is the difference between a ratio and a fraction?
A ratio a:b compares two quantities to each other, while the fraction a/(a+b) compares one part to the whole. A class with a 2:3 ratio of boys to girls is 2/5 boys — not 2/3.